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JBMO Shortlist 2020 N4

Source: JBMO Shortlist 2020

July 4, 2021
JuniorBalkanshortlist2020number theoryprime numbers

Problem Statement

Find all prime numbers pp such that
(x+y)19−x19−y19(x + y)^{19} - x^{19} - y^{19}
is a multiple of pp for any positive integers xx, yy.
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